Seleucus was one of the "diadochi" or successors of Alexander. His name was given to the empire he and his successors ruled. These, the Seleucids, may be familiar because theyl came into contact with the Hellenistic Jews involved in the revolt of the Maccabees (at the heart of the holiday of Hanukkah).
Seleucus himself was one of the Macedonians who fought with Alexander the Great as he conquered Persia and the western part of the Indian subcontinent, from 334 on. His father, Antiochus, had fought with Alexander's father, Philip, and so it is thought Alexander and Seleucus were around the same age, with Seleucus' birthdate about 358. His mother was Laodice. Starting his military career while still a young man, Seleucus had become a senior officer by 326, in command of the royal Hypaspistai and on Alexander's staff. He crossed the Hydaspes River, in the Indian subcontinent, along with Alexander, Perdiccas, Lysimachus, and Ptolemy, some of his fellow notables in the empire carved by Alexander. Then, in 324, Seleucus was among those Alexander required to marry Iranian princesses. Seleucus married Apama, daughter of Spitamenes. Appian says Seleucus founded three cities that he named in her honor. She would become the mother of his successor, Antiochus I Soter. This makes the Seleucids part Macedonian and part Iranian, and so, Persian.
Perdiccas appointed Seleucus "commander of the shield bearers" in about 323, but Seleucus was one of those who murdered Perdiccas. Later, Seleucus resigned command, surrendering it to Cassander, son of Antipater so that he could govern as satrap the province of Babylonia when the territorial division was made at Triparadisus in about 320.
In c. 315, Seleucus fled from Babylonia and Antigonus Monophthalmus to Egypt and Ptolemy Soter.
"One day Seleucus insulted an officer without consulting Antigonus, who was present, and Antigonus out of spite asked for accounts of his money and his possessions; Seleucus, being no match for Antigonus, withdrew to Ptolemy in Egypt. Immediately after his flight, Antigonus deposed Blitor, the governor of Mesopotamia, for letting Seleucus escape, and took over personal control of Babylonia, Mesopotamia and all the peoples from the Medes to the Hellespont...."- Arrian
In 312, at the Battle of Gaza, in the third Diadoch War, Ptolemy and Seleucus defeated Demetrius Polorcetes, son of Antigonus. The next year Seleucus took Babylonia back. When the Babylonian War broke out, Seleucus defeated Nicanor. In 310 he defeated Demetrius. Then Antigonus invaded Babylonia. In 309 Seleucus defeated Antigonus. This marks the start of the Seleucid empire. Then in the Battle of Ipsus, during the fourth Diadoch war, Antigonus was defeated, Seleucus conquered Syria.
"After Antigonus had fallen in battle , the kings who had joined with Seleucus in destroying Antigonus, shared out his territory. Seleucus obtained then Syria from the Euphrates to the sea and inland Phrygia . Always lying in wait for the neighboring peoples, with the power to coerce and the persuasion of diplomacy, he became ruler of Mesopotamia, Armenia, Seleucid Cappadocia (as it is called) , the Persians, Parthians, Bactrians, Arians and Tapurians, Sogdia, Arachosia, Hyrcania, and all other neighboring peoples whom Alexander had conquered in war as far as the Indus. The boundaries of his rule in Asia extended further than those of any ruler apart from Alexander; the whole land from Phrygia eastwards to the river Indus was subject to Seleucus. He crossed the Indus and made war on Sandracottus , king of the Indians about that river, and eventually arranged friendship and a marriage alliance with him. Some of these achievements belong to the period before the end of Antigonus, others to after his death. [...]"- Appian
In September 281, Ptolemy Keraunos assassinated Seleucus, who was buried in a city he had founded and named for himself.
"Seleucus had 72 satraps under him , so vast was the territory he ruled. Most of it he handed over to his son , and ruled himself only the land from the sea to the Euphrates. His last war he fought against Lysimachus for the control of Hellespontine Phrygia; he defeated Lysimachus who fell in the battle, and crossed himself the Hellespont . As he was marching up to Lysimachea  he was murdered by Ptolemy nicknamed Keraunos who was accompanying him ."
This Keraunos was the son of Ptolemy Soter and Eurydice the daughter of Antipater; he had fled from Egypt through fear, as Ptolemy had in mind to hand over his realm to his youngest son. Seleucus welcomed him as the unfortunate son of his friend, and supported and took everywhere his own future assassin. And so Seleucus met his fate at the age of 73, having been king for 42 years."
- Diodorus xviii Justin xiii
- Jona Lendering
- Curtius x.5.7 f